We describe a fast, approximate method to characterize the orbits of satellites around a central binary in numerical simulations. A goal is to distinguish the free eccentricity -- random motion of a satellite relative to a dynamically cool orbit -- from oscillatory modes driven by the central binary's time-varying gravitational potential. We assess the performance of the method using the Kepler-16, Kepler-47, and Pluto-Charon systems. We then apply the method to a simulation of orbital damping in a circumbinary environment, resolving relative speeds between small bodies that are slow enough to promote mergers and growth. These results illustrate how dynamical cooling can set the stage for the formation of Tatooine-like planets around stellar binaries and the small moons around the Pluto-Charon binary planet.

中文翻译：

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关于环绕轨道性质的估计

我们描述了一种快速、近似的方法来表征数值模拟中围绕中心双星的卫星轨道。一个目标是区分自由偏心率——卫星相对于动态冷却轨道的随机运动——与由中央双星随时间变化的引力势驱动的振荡模式。我们使用 Kepler-16、Kepler-47 和 Pluto-Charon 系统评估该方法的性能。然后，我们将该方法应用于环双星环境中轨道阻尼的模拟，解决小天体之间的相对速度，这些小天体的速度足够慢以促进合并和增长。这些结果说明了动态冷却如何为恒星双星周围的类塔图因行星和冥王星-卡戎双星周围的小卫星的形成奠定基础。